4.2 Intermolecular Forces

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4.2.1 Introduction

I Intermolecular forces (IMF): the attractions between molecules

1. all intermolecular forces are based on the Coulomb interaction between two charges: $E_{p}=\frac{Q_{1}Q_{2}}{4\pi\epsilon_{0}r}$ (Eq.30)

   1. $E_{p}$ illustrates the potential energy of the ions, $Q_{1}$ and $Q_{2}$ are the charges of two ions, r is the distance between the two ions.

   2. the stronger the charges of the ions, or the smaller the distance between the two ions, the stronger the attraction

   3. remember that attractions lower the potential energy

2. intermolecular forces tend to be much weaker than chemical bonds

II different types of intermolecular forces exist:

1. ion-dipole interaction: $E_{p} \propto \frac{-|z| \mu}{r^{2}}$

2. dipole-dipole interaction: $E_{p} \propto \frac{\mu_{1} \mu_{2}}{r^{3}}$

3. dipole-induced-dipole: $E_{p} \propto \frac{\mu_{1} \alpha_{2}}{r^{6}}$

4. London dispersion forces: $E_{p} \propto \frac{\alpha_{1} \alpha_{2}}{r^{6}}$

   1. Although Eq.30 has an exponent of r of 1, the intermolecular forces seen here all have exponents of r greater than two. This is because Eq.30 illustrates ionic bonding, which is the interaction between two charged ions.

   2. as the intermolecular force gets weaker, its strength becomes much more dependent on the distance between the two molecules

4.2.2 Ion-Dipole forces

III Ion-dipole forces occur when an ion interacts with a polar molecule

1. a key factor of hydration (surrounding ions with water) are ion-dipole forces

   1. hydration allows many ionic solids to dissolve, as ion-dipole forces stabilize the high-energy ions by lowering its energy

   2. small, high charged ions (strong polarizing power) are hydrated more extensively (higher charge allows stronger IMFs) than large, small charged ions (polarizable)

2. although they have significant interactions, they are weaker than chemical bonds as:

   1. the polar molecule charges are partial instead of a full charge like ions

   2. repulsive forces from the like-charged end of the molecule diminish the attractive forces of the opposite-charged end of the molecule.

4.2.3 Dipole-Dipole forces

IV Dipole-dipole forces occur when polar molecules are arranged with opposite charges together

1. the strength of the dipole-dipole force depends on the polarity of the molecules

2. the partial like-charges of each molecule tends to weaken the attractive force from partial opposite-charges and are even weaker than ion- dipole forces.

V The attractions between opposite charges and repulsions between like charges cancel out for rotating polar molecules

1. rotating polar molecules tend to linger in energetically favorable orientations and have a weak net attraction

2. this attraction is $E_{p} \propto \frac{\mu_{1} \mu_{2}}{r^{6}}$

   1. gas molecules tend to rotate (almost) freely and therefore have minimal intermolecular forces between them

   2. in liquids and solids, molecules do not rotate and therefore have stronger dipole- dipole forces than gases

4.2.4 London Forces

VI the existence of London forces is supported by the fact that monoatomic noble gases can exist in the liquid state

1. in order for molecules to come together, there must be some kind of intermolecular force

VII these forces arise from heterogenous electron density for short periods of time

1. remember that electron clouds only represent the probability of a molecule; as electrons are particles, they can never be homogenous in at a given instant

2. This forms a fleeting partial positive and negative charge and induces a neighboring molecule to be polarized as well (and so on)

3. London forces depend on the polarizability ($\alpha$) of a molecule and its shape

   1. highly polarizable molecules can have large instantaneous dipole moments and therefore strong London forces.

   2. molecules with a larger surface area allows for greater contact points between molecules and therefore stronger London forces.

VIII. Dipole-induced-dipole interactions are similar to London forces:

1. the polar molecule induces a temporary dipole on a non-polar molecule

4.2.5 Hydrogen Bonding

IX Hydrogen bonds are a special case of dipole-dipole interaction

1. A very electronegative atom pulls electron density away from the hydrogen, making the hydrogen atom unshielded, or very low in electron density

2. this little electron density leads to a rather high degree of partial positive charge

3. traditionally, it was thought that hydrogen bonding occurred when the hydrogen atom was connected to nitrogen, oxygen, or fluorine atom with a lone pair

4. the modern definition of hydrogen bonding simply requires the electronegativity difference between hydrogen and the fragment component to be high

X There are many types of hydrogen bonding:

1. acetic acids often exist in the vapor phase as dimers due to H-bonding (Ref. Figure 44)

2. hydrogen fluoride exists in long chains or $(HF)_6$ rings in the gas phase (Ref. Figure 43)

3. intramolecular hydrogen bonding may occur as well (Ref. Figure 42)

4.2.6 Repulsions

XI Although the molecular orbital theory was mainly used to illustrate bonding in prior sections, it can be used to illustrate repulsions as well:

1. consider two helium molecules as they come closer together:

   

2. because an antibonding orbital increases the energy slightly more than a bonding orbital decreases the energy, there is a net increase in energy with smaller distance (Ref. 3.5.3)

3. this increase in energy forces the molecules to repel each other to return to a lower energy state.

XII Repulsions drastically increase as distance decreases as increasing orbital overlap leads to stronger repulsions

XIII Repulsions exponentially decrease as distance increases.